http://www.ck12.org Chapter 9. Rotational Motion
9.1 The Big Idea
The third conservation law isconservation of angular momentum.This vector quantity is the product of rotational
velocity and rotational inertia. In any closed system (including the universe) the quantity of angular momentum is
fixed. Angular momentum can be transferred from one body to another, but cannot be lost or gained. If a system
has its angular momentum changed from the outside it is caused by a torque. Torque is a force applied at a distance
from the center of rotation.
Key Concepts
- To determine therotation axis,wrap your right hand’s fingers in the direction of rotation and your thumb will
point along the axis (see figure). - When something rotates in a circle, it moves through aposition angleθthat runs from 0 to 2πradians and
starts over again at 0. The physical distance it moves is called thepath length.If the radius of the circle is
larger, the path length traveled is longer. - The angular velocityωtells you how quickly the angleθchanges. In more formal language, the rate of change
ofθ, the angular position, is called the angular velocityω. The direction of angular velocity is either clockwise
or counterclockwise. Analogously, the rate of change ofωis the angular accelerationα. - The linear velocity and linear acceleration of rotating object also depend on the radius of rotation, which is
called themoment arm(See figure below.) If something is rotating at a constant angular velocity, it moves
more quickly if it is farther from the center of rotation. For instance, people at the Earth’s equator are moving
faster than people at northern latitudes, even though their day is still 24 hours long –this is because they have
a greater circumference to travel in the same amount of time.